/*
** FFT and FHT routines
** Copyright 1988, 1993; Ron Mayer
**
** fht(fz,n);
** Does a hartley transform of "n" points in the array "fz".
**
** NOTE: This routine uses at least 2 patented algorithms, and may be
** under the restrictions of a bunch of different organizations.
** Although I wrote it completely myself; it is kind of a derivative
** of a routine I once authored and released under the GPL, so it
** may fall under the free software foundation's restrictions;
** it was worked on as a Stanford Univ project, so they claim
** some rights to it; it was further optimized at work here, so
** I think this company claims parts of it. The patents are
** held by R. Bracewell (the FHT algorithm) and O. Buneman (the
** trig generator), both at Stanford Univ.
** If it were up to me, I'd say go do whatever you want with it;
** but it would be polite to give credit to the following people
** if you use this anywhere:
** Euler - probable inventor of the fourier transform.
** Gauss - probable inventor of the FFT.
** Hartley - probable inventor of the hartley transform.
** Buneman - for a really cool trig generator
** Mayer(me) - for authoring this particular version and
** including all the optimizations in one package.
** Thanks,
** Ron Mayer; [email protected]
** and added some optimization by
** Mather - idea of using lookup table
** Takehiro - some dirty hack for speed up
*/
/* $Id: fft.c,v 1.17 2001/01/13 12:54:41 takehiro Exp $ */
#ifdef HAVE_CONFIG_H
# include <config.h>
#endif
#include <math.h>
#include "util.h"
#include "fft.h"
#ifdef WITH_DMALLOC
#include <dmalloc.h>
#endif
#ifndef USE_FFT3DN
#define TRI_SIZE (5-1) /* 1024 = 4**5 */
static const FLOAT costab[TRI_SIZE*2] = {
9.238795325112867e-01, 3.826834323650898e-01,
9.951847266721969e-01, 9.801714032956060e-02,
9.996988186962042e-01, 2.454122852291229e-02,
9.999811752826011e-01, 6.135884649154475e-03
};
inline static void fht(FLOAT *fz, int n)
{
const FLOAT *tri = costab;
int k4;
FLOAT *fi, *fn, *gi;
fn = fz + n;
k4 = 4;
do {
FLOAT s1, c1;
int i, k1, k2, k3, kx;
kx = k4 >> 1;
k1 = k4;
k2 = k4 << 1;
k3 = k2 + k1;
k4 = k2 << 1;
fi = fz;
gi = fi + kx;
do {
FLOAT f0,f1,f2,f3;
f1 = fi[0] - fi[k1];
f0 = fi[0] + fi[k1];
f3 = fi[k2] - fi[k3];
f2 = fi[k2] + fi[k3];
fi[k2] = f0 - f2;
fi[0 ] = f0 + f2;
fi[k3] = f1 - f3;
fi[k1] = f1 + f3;
f1 = gi[0] - gi[k1];
f0 = gi[0] + gi[k1];
f3 = SQRT2 * gi[k3];
f2 = SQRT2 * gi[k2];
gi[k2] = f0 - f2;
gi[0 ] = f0 + f2;
gi[k3] = f1 - f3;
gi[k1] = f1 + f3;
gi += k4;
fi += k4;
} while (fi<fn);
c1 = tri[0];
s1 = tri[1];
for (i = 1; i < kx; i++) {
FLOAT c2,s2;
c2 = 1 - (2*s1)*s1;
s2 = (2*s1)*c1;
fi = fz + i;
gi = fz + k1 - i;
do {
FLOAT a,b,g0,f0,f1,g1,f2,g2,f3,g3;
b = s2*fi[k1] - c2*gi[k1];
a = c2*fi[k1] + s2*gi[k1];
f1 = fi[0 ] - a;
f0 = fi[0 ] + a;
g1 = gi[0 ] - b;
g0 = gi[0 ] + b;
b = s2*fi[k3] - c2*gi[k3];
a = c2*fi[k3] + s2*gi[k3];
f3 = fi[k2] - a;
f2 = fi[k2] + a;
g3 = gi[k2] - b;
g2 = gi[k2] + b;
b = s1*f2 - c1*g3;
a = c1*f2 + s1*g3;
fi[k2] = f0 - a;
fi[0 ] = f0 + a;
gi[k3] = g1 - b;
gi[k1] = g1 + b;
b = c1*g2 - s1*f3;
a = s1*g2 + c1*f3;
gi[k2] = g0 - a;
gi[0 ] = g0 + a;
fi[k3] = f1 - b;
fi[k1] = f1 + b;
gi += k4;
fi += k4;
} while (fi<fn);
c2 = c1;
c1 = c2 * tri[0] - s1 * tri[1];
s1 = c2 * tri[1] + s1 * tri[0];
}
tri += 2;
} while (k4<n);
}
#else
#define fht(a,b) fht_3DN(a,b/2)
#endif /* USE_FFT3DN */
static const unsigned char rv_tbl[] = {
0x00, 0x80, 0x40, 0xc0, 0x20, 0xa0, 0x60, 0xe0,
0x10, 0x90, 0x50, 0xd0, 0x30, 0xb0, 0x70, 0xf0,
0x08, 0x88, 0x48, 0xc8, 0x28, 0xa8, 0x68, 0xe8,
0x18, 0x98, 0x58, 0xd8, 0x38, 0xb8, 0x78, 0xf8,
0x04, 0x84, 0x44, 0xc4, 0x24, 0xa4, 0x64, 0xe4,
0x14, 0x94, 0x54, 0xd4, 0x34, 0xb4, 0x74, 0xf4,
0x0c, 0x8c, 0x4c, 0xcc, 0x2c, 0xac, 0x6c, 0xec,
0x1c, 0x9c, 0x5c, 0xdc, 0x3c, 0xbc, 0x7c, 0xfc,
0x02, 0x82, 0x42, 0xc2, 0x22, 0xa2, 0x62, 0xe2,
0x12, 0x92, 0x52, 0xd2, 0x32, 0xb2, 0x72, 0xf2,
0x0a, 0x8a, 0x4a, 0xca, 0x2a, 0xaa, 0x6a, 0xea,
0x1a, 0x9a, 0x5a, 0xda, 0x3a, 0xba, 0x7a, 0xfa,
0x06, 0x86, 0x46, 0xc6, 0x26, 0xa6, 0x66, 0xe6,
0x16, 0x96, 0x56, 0xd6, 0x36, 0xb6, 0x76, 0xf6,
0x0e, 0x8e, 0x4e, 0xce, 0x2e, 0xae, 0x6e, 0xee,
0x1e, 0x9e, 0x5e, 0xde, 0x3e, 0xbe, 0x7e, 0xfe
};
#define ch01(index) (buffer[chn][index])
#define ml00(f) (window[i ] * f(i))
#define ml10(f) (window[i + 0x200] * f(i + 0x200))
#define ml20(f) (window[i + 0x100] * f(i + 0x100))
#define ml30(f) (window[i + 0x300] * f(i + 0x300))
#define ml01(f) (window[i + 0x001] * f(i + 0x001))
#define ml11(f) (window[i + 0x201] * f(i + 0x201))
#define ml21(f) (window[i + 0x101] * f(i + 0x101))
#define ml31(f) (window[i + 0x301] * f(i + 0x301))
#define ms00(f) (window_s[i ] * f(i + k))
#define ms10(f) (window_s[0x7f - i] * f(i + k + 0x80))
#define ms20(f) (window_s[i + 0x40] * f(i + k + 0x40))
#define ms30(f) (window_s[0x3f - i] * f(i + k + 0xc0))
#define ms01(f) (window_s[i + 0x01] * f(i + k + 0x01))
#define ms11(f) (window_s[0x7e - i] * f(i + k + 0x81))
#define ms21(f) (window_s[i + 0x41] * f(i + k + 0x41))
#define ms31(f) (window_s[0x3e - i] * f(i + k + 0xc1))
void fft_short(lame_internal_flags *gfc,
FLOAT x_real[3][BLKSIZE_s], int chn, const sample_t *buffer[2])
{
const FLOAT* window_s = (const FLOAT *)&gfc->window_s[0];
int i;
int j;
int b;
for (b = 0; b < 3; b++) {
FLOAT *x = &x_real[b][BLKSIZE_s / 2];
short k = (576 / 3) * (b + 1);
j = BLKSIZE_s / 8 - 1;
do {
FLOAT f0,f1,f2,f3, w;
i = rv_tbl[j << 2];
f0 = ms00(ch01); w = ms10(ch01); f1 = f0 - w; f0 = f0 + w;
f2 = ms20(ch01); w = ms30(ch01); f3 = f2 - w; f2 = f2 + w;
x -= 4;
x[0] = f0 + f2;
x[2] = f0 - f2;
x[1] = f1 + f3;
x[3] = f1 - f3;
f0 = ms01(ch01); w = ms11(ch01); f1 = f0 - w; f0 = f0 + w;
f2 = ms21(ch01); w = ms31(ch01); f3 = f2 - w; f2 = f2 + w;
x[BLKSIZE_s / 2 + 0] = f0 + f2;
x[BLKSIZE_s / 2 + 2] = f0 - f2;
x[BLKSIZE_s / 2 + 1] = f1 + f3;
x[BLKSIZE_s / 2 + 3] = f1 - f3;
} while (--j >= 0);
fht(x, BLKSIZE_s);
}
}
void fft_long(lame_internal_flags * const gfc,
FLOAT x[BLKSIZE], int chn, const sample_t *buffer[2] )
{
const FLOAT* window = (const FLOAT *)&gfc->window[0];
int i;
int jj = BLKSIZE / 8 - 1;
x += BLKSIZE / 2;
do {
FLOAT f0,f1,f2,f3, w;
i = rv_tbl[jj];
f0 = ml00(ch01); w = ml10(ch01); f1 = f0 - w; f0 = f0 + w;
f2 = ml20(ch01); w = ml30(ch01); f3 = f2 - w; f2 = f2 + w;
x -= 4;
x[0] = f0 + f2;
x[2] = f0 - f2;
x[1] = f1 + f3;
x[3] = f1 - f3;
f0 = ml01(ch01); w = ml11(ch01); f1 = f0 - w; f0 = f0 + w;
f2 = ml21(ch01); w = ml31(ch01); f3 = f2 - w; f2 = f2 + w;
x[BLKSIZE / 2 + 0] = f0 + f2;
x[BLKSIZE / 2 + 2] = f0 - f2;
x[BLKSIZE / 2 + 1] = f1 + f3;
x[BLKSIZE / 2 + 3] = f1 - f3;
} while (--jj >= 0);
fht(x, BLKSIZE);
}
void init_fft(lame_internal_flags * const gfc)
{
FLOAT *window = &gfc->window[0];
FLOAT *window_s = &gfc->window_s[0];
int i;
#if 0
if (gfc->nsPsy.use) {
for (i = 0; i < BLKSIZE ; i++)
/* blackman window */
window[i] = 0.42-0.5*cos(2*PI*i/(BLKSIZE-1))+0.08*cos(4*PI*i/(BLKSIZE-1));
} else {
/*
* calculate HANN window coefficients
*/
for (i = 0; i < BLKSIZE ; i++)
window[i] = 0.5 * (1.0 - cos(2.0 * PI * (i + 0.5) / BLKSIZE));
}
#endif
// The type of window used here will make no real difference, but
// in the interest of merging nspsytune stuff - switch to blackman window
for (i = 0; i < BLKSIZE ; i++)
/* blackman window */
window[i] = 0.42-0.5*cos(2*PI*(i+.5)/BLKSIZE)+
0.08*cos(4*PI*(i+.5)/BLKSIZE);
for (i = 0; i < BLKSIZE_s/2 ; i++)
window_s[i] = 0.5 * (1.0 - cos(2.0 * PI * (i + 0.5) / BLKSIZE_s));
}
|
